Question

Explain how to use the pairs found in Exercise 51 to add 4 and 7.

Short answer

Adding 4 and 7 gives (2,1) which corresponds 11.

Step-by-step solution

Step: 1

Find 4 mod 3 and 4 mod 5

$\begin{array}{r}4mod3=1\\ 4mod5=4\\ (1,4)\end{array}$

Step: 2

Find 7mod 3 and 7 mod 5

$\begin{array}{r}7mod3=1\\ 7mod5=2\\ (1,2)\end{array}$

Step: 3

Add 4 and 7

$(1,4)+(1,2)=(2,1)$

Since 4+2=6 but 6 mod 5 =1

So, (2,1) corresponds to 11.